Often there are multiple reports of gloom and doom about connections at Heathrow. I have just had a very easy and quick experience.
5 minute walk from my gate to the flight connections bus to switch to terminal 3. 5 minute wait for bus. 8 minute ride to terminal 3 . 10 minutes to get through security and into terminal waiting area.
Now I realize it isn’t always this smooth, but I wanted to point out that Heathrow transfers are not necessarily difficult and long every time.